Euler numbers

The Euler numbers $E_k$ are the coefficients in the following Taylor series for $|z| < \dfrac{\pi}{2}$:
$$\mathrm{sech}(z) = \displaystyle\sum_{k=0}^{\infty} E_k \dfrac{z^n}{n!},$$
where $\mathrm{sech}$ denotes hyperbolic secant.